# Questions tagged [lie-groupoids]

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11 questions
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### Differentiation of Lie $\infty$-groupoids

I've been trying to understand how to differentiate Lie $\infty$-groupoids to get a Lie $\infty$-algebroid. First of all, I will state the definitions that I'm assuming. A Lie $\infty$-groupoid is a ...
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### On Holonomy in (regular) Riemannian Foliations

Right now, I am trying to understanding the role of holonomy fields on Riemannian foliations, which lead me to the following (probably topological) groupoid: Let $\mathcal{F}\subset M$ be a ...
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### KK-witnesses of Gysin maps between differentiable stacks

In 1982 Alain Connes gave the construction of a KK-element $f! \in KK(C(X), C(Y))$ that "witnesses" the fiber integration/Gysin/Umkehr/wrong-way map on topological $K$-theory along a K-orientable map ...
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### Is this groupoid a model for the derived fixed-point locus of the free loop space?

In this paper, John Baez and Urs Schreiber define (see Definition 2.16) a Lie groupoid (there called a '2-space') associated to any manifold $M$. In fact it is a bundle of Lie groups over $M$ thought ...
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### Action of a Lie groupoid on a Lie Algebroid?

Let $\pi:E\longrightarrow M$ be a vector bundle. Then we can associate a Lie groupoid $\mathsf{Gl}(E)\rightrightarrows M$ where \mathsf{Gl}(E):=\{E_x\stackrel{lin. isom.}{\longrightarrow} E_y: x, y\...
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### Which makes Lie groupoids so nice?

This is a continuation of my previous question. A) Morphisms in (1') are basically internal anafunctors, their compositions heavily use (and only) pullback/limit. B) Bibundles in (2) are basically ...
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### Idea behind definition of classifying space over an orbifold

Today I was explaining to some one the notion of $\mathcal{G}$ spaces, covering spaces over orbifolds from Orbifolds as Groupoids: an Introduction. Definition : Let $X$ be a locally compact ...
This question came from comments of this question. Suppose $\mathcal{G}$ is a Lie groupoid, we consider the category $B\mathcal{G}$ whose objects are principal $\mathcal{G}$ bundles and morphisms are ...